Microlithography and electron beam writing are examples of applications that generate precise patterns on a sample, such as a semiconductor wafer or mask. Such applications require accurate placement and/or movement of the sample stage relative to the writing tool. Often, accurate positioning of different components within the writing tool, such as the relative position of a reticle in a lithography tool, also requires accurate positioning.
To enable such accurate positioning, heterodyne distance measuring interferometers are often used to measure distance changes along one or more axes. The distance measurements can provide a control signal that drives a servo system for accurately positioning different components of a given system.
A heterodyne distance measuring interferometer measures chances in the position of a measurement object relative to a reference object based on optical interference generated by overlapping and interfering a measurement beam reflected from a measurement object with a reference beam. Measurement of the optical interference produces an interference intensity signal that oscillates at a heterodyne angular frequency ω corresponding to small difference in frequency between the measurement and reference beams. Changes in the relative position of the measurement object correspond to changes in the phase φ of the oscillating intensity signal, with a 2π phase change substantially equal to a distance change L of λ/(np), where L is a round-trip distance change, e.g., the change in distance to and from a stage that includes the measurement object, λ is the wavelength of the measurement and reference beams, n is the refractive index of the medium through which the light beams travel, e.g., air or vacuum, and p is the number of passes to the reference and measurement objects.
Unfortunately, this equality is not always exact. Many interferometers include non-linearities such as what are known as “cyclic errors.” Some cyclic errors can be expressed as contributions to the phase and/or the intensity of the measured interference signal and have a sinusoidal dependence on the change in optical path length pnL. In particular, the first harmonic cyclic error in phase has a sinusoidal dependence on (2πpnL)/λ and the second harmonic cyclic error in phase has a sinusoidal dependence on 2(2πpnL)/λ. Higher order and sub-harmonic cyclic errors can also be present.